Question

What is the motional EMF across a small element \[dr\] of a rotating rod?

Options

• \[d\varepsilon=B\omega\,dr/r\]

• \[d\varepsilon=Bv\,dr=B\omega r\,dr\]

• \[d\varepsilon=B\omega R^2\,dr\]

• \[d\varepsilon=Br\,dr/\omega\]

Answer 1

Apply the motional emf formula to the small length \[dr\]: \[d\varepsilon=Bv\,dr\]. Since its velocity is \[v=\omega r\], this becomes \[d\varepsilon=B\omega r\,dr\].